Check all shields covers etc for loose bolts. I had a similar rattle on my 06 at certain revs and it turned out to be the bearclaw.
Goth is right plus check the radiator shrouds the lower one has been known to be a hidden noise. plus heat shield on the exhaust. Otherwise its time to check the timing chain tensioner drop to see if it is all the way extended or maybe it needs the triumph spacer added. two return the soring tension requiered to hold the tensioner out at the proper tension.
This is done with the engine not running and do not turn it over until it is back together.
Triumph makes a nylon plug tool that comes with the space the check the drop of the plunger in the tensioner after 16mm it is required to add a spacer inside the plunger increasing the tension on the spring that pushes the plunger out into the guide keeping proper tension on the timing chain. so I tdoes not rattle and lessons the chance of the tensioner pushing back in causing a timing shift and damagine the valves.
Here is a shot of the procedure in the manual
if this plastic tool/plug bottoms out you need to add the spacer but instead of spending the money when it might not be the case you can check the drop first and then order or make the spacer yourself.
Firt thing to do is withe the engien off place the bike in say third gear stand it up and rock it back and forth a few times like forward and then back forward and then back. without pulling the clutch handle in so you won't be able to do anything but rock the bike. this will alow the tensioner to adjust if needed. Next put the kick stand down and remove the center nut on the tensioner this is the large one in the center
AS WE ARE NOT REMOVING THE TENSIONER with the center nut out
NEVER TURN ENGINE OVER WITh THE STARTER OR TRY TO MOVE THE BIKE Now with a set of Dial calipers measure the drop to the shoulder of the plunger in the tensioner like in the picture below
If the measurement is 16 mm or more thats .629" or a **** hair over 5/8 inch for us mericans it needs the spacer in the plunger. It goes inside the center of the plunger and can be mad by a 10 mm bolt use the shank portion cut a piece .350" inch long and stick it in there then put the center nut along with the spring on the rod and the large copper waser back in and torque to specifications. ( Note make sure you do the measurement without the copper was stuck to the body of the tensioner or it will freak you out

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The total possible drop of the tensioner is 26.39 mm or 1.039" inch. If your measure ment is very deap then it is time to renew the timing chain and tensioner guide. A good time to havve the valves shims checked and changed if needed.
Below is a picture of the parts that you will be pulling out to do these checks. The manual says you should change the copper washer but to be honest I never have
Just make sure the copper washer is not on the body when you do the measurement or you will measure a drop plus the thickness of the washer.
I believe Triumph changed the size of material and or the arc of the new guide tensinoner side to lesson the amount the tensioner drops. I am working on another modification to the tensioner so you will not have to renew the chain as fast and will be able to do the tensiner chnage/mod without pulling anything but the cam cover. But it is only an idea at this time and when I get new stronger head bolts for the Falcon I will look into it as I disassemble her so it will be a little while before I have it done and proved out. Lets just say right now it is on a drawing in my head
Anyway hope this helps you out Glenn good luck any questions do not be afraid to ask.